A useful measure of how hard, or perhaps a better word to use is challenging, a game is would be to look at the strength differential between good players and weak players.
Challenging games tend to have tactical and strategic subtlety (depth in other words) and strong players can exploit their superior knowledge and vision of these ideas. Equally, weaker players can gradually learn these ideas and improve.
So I would define a game as being hard if there is a broad range in standards of play. This would imply that games like chess and go and poker and maybe even scrabble are hard games.
Games like tic-tac-toe and snakes and ladders are not.
So, Mr. DimebagdDerek, do either game help the other or are they so different there is no cross over? I assume it's like going from the piano to the kazoo, or vice versa.
No, I don't think the difference between chess and checkers is equal to the piano and the kazoo. No offense intended.